1. Field of the Invention
The present invention relates to a relief type diffraction optical element comprising a substrate having a surface in which a given relief pattern is formed, an optical system comprising such a relief type diffraction optical element, an optical apparatus comprising such an optical system, and a mold for manufacturing the relief type diffraction optical element.
2. Description of the Related Art
In accordance with a recent tendency of miniaturization of optical systems, a relief type diffraction optical element such as a diffraction grating type lens has been watched, because the relief type diffraction grating can be made small in size and light in weight. For instance, the relief type diffractive lens is expected to be utilized in various fields due to the fact that chromatic aberration can be corrected effectively and aspherical performance can be attained easily.
It should be noted that the diffraction type lens means an optical element in which the lens function of a conventional refraction type lens such as a spherical lens, cylindrical lens and anamorphic lens is realized by the diffraction. For instance, a diffractive lens corresponding to the spherical lens includes a grating pattern of a plurality of concentric ring-shaped portions, and a diffraction type lens corresponding to the cylindrical lens comprises a rectilinear grating pattern. In the present specification, one groove of such a grating pattern is called a zone, and a zone at an optical axis of the diffraction type lens is termed as a first zone and successively outgoing zones are termed as second zone, third zone and so on.
When a parallel light flux is collected at a point by means of a lens, a phase shift function of this lens may be expressed by the following equation (1):φ(r)=−πr2/(λf)  (1)     r: distance from optical axis    λ: wavelength    f: focal length
When the angle φ(r) is transformed into a phase structure of 2π, a phase shift function φd(r) of the diffraction type lens may be expressed by the following equation.φd(r)=φ(r)+2π(i−1)  (2) RI-1<r<RI (i=1, 2, 3 . . . ) 
This equation (2) means that the diffraction efficiency is optimized for the first-order diffraction. Here, Ri is an outer radius of an ith zone. FIG. 1 shows the phase shift function φ(r) of the lens and the phase shift function FIG. 1 shows the phase shift function φd(r) of the diffraction type lens. It should be noted that a distance between outer radii of adjacent zones is termed as a pitch. A central zone of the diffraction type lens has a maximum width or pitch which is equal to a radius.
When the diffraction type lens is realized by the relief structure following the phase shift function, a height t(r) of the relief structure at a radius r may be expressed by the following equation.t(r)=tg·[{φd(r)/2π}+1]  (3) Here, tg is the maximum depth of the relief structure and may be represented as follows:tg=λ/(n−1)  (4) wherein, n is a refractive index of a material of which a diffraction optical element is made.
It should be noted that the above equation (2) represents the phase shift function of the diffraction type lens which converges a parallel light flux at a point by means of a single diffraction type lens. When a diffraction type lens is used in combination with other optical element, e.g. a refraction type lens, a phase shift function of the diffraction type lens is generally expressed by a polynomial equation of even higher orders.
In JP-A Kokai Hei 1-250902, there is proposed a known diffraction optical element, in which all zones are formed to have an ideal curvilinear cross sectional configuration which follows a phase shift function. This known diffraction optical element has a sufficiently high optical performance.
In Japanese technical magazine, “Optical Technique Contact”, Vol. 26, No. 3, pp. 208-212, there is described another known diffraction optical element, in which all zones are formed to have a rectilinear cross sectional configuration which approximates to an ideal curvilinear configuration following a phase shift function. Such a diffraction optical element can be manufactured easily.
The relief type diffraction optical element may be manufactured by various methods. In one manufacturing method, use is made of a mold with a bottom wall having a cross sectional configuration which is inverse to a relief pattern of a relief type diffraction optical element to be formed. The mold is pushed against a softened optical glass or plastic material to transfer the relief pattern of the bottom wall of the mold to the surface of the material. Alternatively, the relief pattern of the bottom wall of the mold may be transferred to an optical material by means of the injection molding method or photo-polymer method. In the above mentioned “Optical Technique Contact”, Vol. 26, No. 3, page 212, there is proposed a known mold for manufacturing the relief type diffraction optical element, in which all zones of a relief pattern of the mold are formed to have a rectilinear configuration which approximates to an ideal curvilinear configuration following the phase shift function. It is apparent that such a mold can be manufactured easily.
FIG. 2 is a schematic cross sectional view showing a known relief type diffraction optical element, in which all zone are formed to have an ideal curvilinear cross sectional configuration which follows a given phase shift function. However, it is rather difficult to manufacture and check such a curvilinear cross sectional configuration. Moreover, a working time and a checking time are liable to be long. For instance, when an optical material is treated to have an ideal curvilinear cross sectional configuration by cutting, it is necessary to perform the cutting by means of a tip of a cutting edge of a byte. Then, it is difficult to obtain a good surface roughness as compared with a case in which the relief pattern is formed by using a whole length of the cutting edge.
In order to mitigate the above mentioned problem, there has been proposed another known relief type diffraction optical element shown in FIG. 3. In this known diffraction type lens, all zones are formed to have a rectilinear cross sectional configuration denoted by a solid line 3 in FIG. 3, said rectilinear configuration approximating an ideal curvilinear cross sectional configuration denoted by a broken line 4 which follows the phase shift function. This rectilinear configuration has great advantages in view of the manufacturing and checking operation. For instance, when the rectilinear configuration is formed by cutting, it is possible to use a whole length of the cutting edge, and therefore working date can be simplified and a good surface roughness can be attained.
However, when the rectilinear configuration is used for all zones, there is another problem that the optical performance is degraded as will be explained hereinbelow. Particularly, when the number of zones is small, the degradation of the optical performance might become very large.
Now it is assumed that a diffraction type lens having a focal length f is formed such that all zones have a rectilinear cross sectional configuration, and a parallel light flux having a wavelength x is made incident upon the diffraction type lens. Then, a ratio of an intensity of light IR converged at a focal point of the diffraction type lens to an intensity of light IC converged at a focal point of the ideal diffraction type lens having a focal length f and an ideal curvilinear cross sectional configuration is considered. This ratio of light intensity at the focal point may be expressed as follows.Ratio of light intensity=IR/IC  (5) 
FIG. 4 is a graph showing a variation of the ratio of the intensity of light IR/IC in accordance with the number of zones. As can be seen from the graph of FIG. 4, when the number of zones is large, the optical performance of the diffraction type lens having the rectilinear cross sectional configuration is not decreased so much, but the number of zones is small, the light intensity at the focal point is reduced to a large extent. This phenomenon could not be ignored when the number of zones through which light transmits is small like as a case in which a micro-lens or an image forming lens is used together with a stop.
Therefore, in an optical system constructed by using the relief type diffraction optical element, when light is made incident upon a small number of zones of the relief type diffraction optical element, a light intensity at a focal point is reduced to a large extent, and since a focussed spot expands laterally, MTF is reduced and a resolution is decreased.
In case of forming a mold for manufacturing a relief type diffraction optical element, it is desirable that the mold has a cross sectional configuration corresponding to a phase shift function of a relief type diffraction optical element to be manufactured. However, in practice, it is quite difficult to form a cross sectional configuration of the mold in accordance with a desired curvilinear shape. Therefore, all zones of a known mold are formed to have a rectilinear cross sectional configuration which approximates an ideal curvilinear cross sectional configuration. It is apparent that a relief type diffraction optical element manufactured by using such a mold has a corresponding rectilinear cross sectional configuration and its optical performance is degraded.
Furthermore, when a mold is manufactured by a lathe, in order to form a curvilinear cross sectional configuration, it is necessary to use only a tip of a cutting edge of a byte. In general, since a material of a mold is hardly worked, it is difficult to finish a mold surface as a mirror surface by means of such working. Therefore, a relief type diffraction optical element manufactured by such a mold has a large surface roughness. Then, a part of incident light is scattered by the diffraction type lens and a utilization efficiency is decreased. Moreover, the scattered light might become undesired stray light and the optical performance is degraded.